Tropical Robinson-Schensted-Knuth correspondence and birational Weyl group actions
Masatoshi Noumi, Yasuhiko Yamada
Abstract
By using an elementary matrix approach, based on the technique of discrete Toda equation, we construct subtraction-free rational and piecewise linear transformations associated with various combinatorial algorithms, including the RSK correspondence. We also investigate birational Weyl group actions related to those algorithms.
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